Quantum Time - Quantum Physics

Abstract: Normally we quantize along the space dimensions but treat time classically.But from relativity we expect a high level of symmetry between time and space.What happens if we quantize time using the same rules we use to quantize space?To do this, we generalize the paths in the Feynman path integral to includepaths that vary in time as well as in space. We use Morlet waveletdecomposition to ensure convergence and normalization of the path integrals. Wederive the Schr\-odinger equation in four dimensions from the short time limitof the path integral expression. We verify that we recover standard quantumtheory in the non-relativistic, semi-classical, and long time limits. Quantumtime is an experiment factory: most foundational experiments in quantummechanics can be modified in a way that makes them tests of quantum time. Welook at single and double slits in time, scattering by time-varying electricand magnetic fields, and the Aharonov-Bohm effect in time.